Developmental hourglass: Verification by numerical evolution and elucidation by dynamical-systems theory

Determining the general laws between evolution and development is a fundamental biological challenge. Developmental hourglasses have attracted increased attention as candidates for such laws, but the necessity of their emergence remains elusive. We conducted evolutionary simulations of developmental processes to confirm the emergence of the developmental hourglass and unveiled its establishment. We considered organisms consisting of cells containing identical gene networks that control morphogenesis and evolved them under selection pressure to induce more cell types. By computing the similarity between the spatial patterns of gene expression of two species that evolved from a common ancestor, a developmental hourglass was observed, that is, there was a correlation peak in the intermediate stage of development. The fraction of pleiotropic genes increased, whereas the variance in individuals decreased, consistent with previous experimental reports. Reduction of the unavoidable variance by initial or developmental noise, essential for survival, was achieved up to the hourglass bottleneck stage, followed by diversification in developmental processes, whose timing is controlled by the slow expression dynamics conserved among organisms sharing the hourglass. This study suggests why developmental hourglasses are observed within a certain phylogenetic range of species.

1.I feel that the phrase in the title "confirmation by numerical simulation" is too strong.The word "confirmed" is also used in the first sentence of Discussion.As far as I can understand, this work successfully generated an hourglass-like developmental process using a simple model.Although the findings are impressive and important, I feel they are still far from "confirmation" of experimental observations.Some weaker expression will be suitable.
2. The morphogen gradient is important for cell differentiation to occur.However, I could not find any mention of the morphogen gradient until I read the Method section.I think it should be mentioned, at least briefly, before the results are described.Otherwise, readers also may be confused about the origin of cell differentiation.Also, the number of cells, M, is not provided even in Method (I only found it's more than 120 from the Figures).

Fig2
. A2 is for one individual that has a common ancestor with the individual shown in A1.Other examples from the same simulation (is it right?)are shown in S2F.But there are a hundred individuals in one population (the number of genotypes may be less).Are they all behave similarly?Although the phrase "always in the middle of ..." is used in the main text, it is still not clear if there is no exception.If all the individuals exhibit hourglass-like behavior when the derivative species are close in the phylogenetic tree, it should be clearly stated.
I feel that the distinction between "examples" and "all" is not taken care of throughout the paper.If all the individuals behave similarly, it should be stated.And if there are exceptions, it also should be mentioned.
4. Seeing Fig. 2 and S2F, I found that the progression patterns of the similarity indicator are diverse between individuals.Then, I wonder how it progresses if the similarity indicator is calculated between individuals in the same species.The result will serve as a reference to estimate the extent of similarity between different species.

Caption of Fig.3
The readers cannot judge if the sentence "In this case, for the pair branched at the recent 100-300 generations" is correct, because only the data for "200 generations (blue)" is shown in the corresponding range, and it seems that the green line (500 generations) also exhibits a peak at the same point.
6.The definition of the pleiotropic genes is unclear.Since the individual has many cells with different cell states, I think the gene expression levels differ from cell to cell.In such a situation, how are the pleiotropic genes identified?Some more detailed explanation is required.

p.14 second paragraph
Although the importance of the noise in the initial condition is stressed for the emergence of the developmental hourglass, I could not find how the noise in the initial state is introduced except for the clone experiment in Fig. 5.
8. p.14 second paragraph (The discussion on the robustness) Although the authors wrote "Hence, during the ...", it is not confirmed in this paper.Thus, this part is not appropriate to be written here.This point should be discussed in Discussion.9. p.15 the last paragraph I could not find a description of how the time scale of the slow genes can be changed.
10. Discussions, 2nd paragraph At the end of the second paragraph, the perturbations in the initial condition is mentioned.But I could not find the description of this perturbation.

Discussions, 6th paragraph
In this paper, the term "species" and "phylum" are used rather arbitrarily in discussing the results.It is not clear how we can define "species" and "phylum" in this model.In this connection, the last sentence "This result corresponds..." seems to be sloppy.
12. Discussions, 7th paragraph.The meaning of the sentence "when such processes..." is unclear.Since the cell interactions described in the former sentence are not investigated in this paper, more reasoning should be written for discussing them.
13. Methods: Gene expression dynamics I think r.h.s. of equation ( 1) may be In eq.( 1), the diffusion is expressed by the spatial second derivative.But in this model, the cell positions are discrete, and the spatial distribution of x i within cells is not considered.Thus the diffusion effect should be described by the difference between neighboring cells rather than the spatial derivative.
14. Methods: Initial/boundary conditions I could not understand the meaning of the sentence "the expression levels of each gene...".
15. Methods: Fitness function ON and OFF are defined as > 0.99 and < 0.01, respectively.Then, there should be the intermediate range of the expression.Seeing Fig 6B, expressions of some genes at the final state take intermediate values.If the final states of the target four genes are always either ON or OFF without exception, it should be mentioned.In that case, the mechanism for target genes to reach either an ON or OFF state should be described briefly.In case some exceptions have been observed, they should also be mentioned.

Methods: Mutation
The list of evolvable parameters is lacking.
Minor points: 1. Fig 2C and 3 The title of the vertical axis should be "similarity indicator".

Fig.5
The definition of the total variance in gene expressions is unclear.
3. P.14 second paragraph Fig. 4 may be Fig. 5 4. Fig. 6 The definition of the variance in the timescale in C is not clear.Are these variances calculated for timescales over different cells?
5. Methods: Calculation of variance... x l should be x i .At the end of the paragraph, there is a summation over j, but I think it should be the summation over i.